function [u] = NewDirichlet(n)
% an example forcing function
g = @(x) 10*sin(pi*x(1))*cos(pi*x(2));
% construct a grid, here the code produces a uniform grid
% this can easily be modified starting from an arbitrary collection of
% points
TR = uniform_grid(n);
% find boundary vertices - often better constructed along with
% triangulation, but for small grids this is adequate
boundary = unique(freeBoundary(TR))';
% first stage of assembly
[A,f] = NewAssemble(TR,g);
% apply boundary conditions
A(boundary,:)=0;
A(:,boundary)=0;
for i = boundary
A(i,i)=1;
end
f(boundary)=0;
% solve system, here using explicit methods
% for large grids, iterative schemes can be employed instead
u = A \ f;
% a plot of the result
p2 = [TR.Points,u];
TR2 = triangulation(TR.ConnectivityList,p2);
trisurf(TR2);